Decomposing variables into between and within components are often required in multilevel analysis. This method of decomposition should not ignore possible unreliability of an observed group mean (i.e., arithmetic mean) that is due to small cluster sizes and can lead to substantially biased estimates. Adjustment procedures that allow unbiased…

This article is premised on the observation that in educational research there is an increasing use of terminology and concepts related to the field of complexity and the study of complex physical, biological, and social systems. As we are at an early stage in this cross-fertilization of complex systems ideas and methods in educational research,…

Changing criterion designs (CCD) are single-case experimental designs that entail a step-by-step approximation of the final level desired for a target behavior. Following a recent review on the desirable methodological features of CCDs, the current text focuses on an analytical challenge: the definition of an objective rule for assessing the…

Sample size determination in multilevel randomized trials (MRTs) and multilevel regression discontinuity designs (MRDDs) can be complicated due to multilevel structure, monetary restrictions, differing marginal costs per treatment and control units, and range restrictions in sample size at one or more levels. These issues have sparked a set of…

Multilevel latent class analysis (MLCA) has been increasingly used to investigate unobserved population heterogeneity while taking into account data dependency. Nonparametric MLCA has gained much popularity due to the advantage of classifying both individuals and clusters into latent classes. This study demonstrated the need to relax the…

The complex dynamical systems (CDS) approach consists of a family of theories emanating largely from the exact sciences. These theories share a common focus on the behavior of systems and their interrelated parts and are concerned with the processes of stability, change, and unpredictability in those systems. This article takes stock of the…

There is a need for effect sizes that are readily interpretable by a broad audience. One index that might fill this need is [pi], which represents the proportion of scores in one group that exceed the mean of another group. The robustness of estimates of [pi] to violations of normality had not been explored. Using simulated data, three estimates…

In this commentary, we propose a framework for applying the Complex Dynamical Systems (CDS) approach in educational research. Drawing on the conceptual articles in the special issue for ontological, theoretical, and methodological principles, and on the empirical articles for examples of these principles' application, we suggest six interdependent…

Lord's Paradox occurs when a continuous covariate is statistically controlled for and the relationship between a continuous outcome and group status indicator changes in both magnitude and direction. This phenomenon poses a challenge to the notion of evidence-based policy, where data are supposed to be self-evident. We examined 50 effect size…

Randomized controlled trials are not always feasible in educational research, so researchers must use alternative methods to study treatment effects. Propensity score matching is one such method for observational studies that has shown considerable growth in popularity since it was first introduced in the early 1980s. This paper outlines the…

Respondent attrition is a common problem in national longitudinal panel surveys. To make full use of the data, weights are provided to account for attrition. Weight adjustments are based on sampling design information and data from the base year; information from subsequent waves is typically not utilized. Alternative methods to address bias from…

Structured means analysis is a very useful approach for testing hypotheses about population means on latent constructs. In such models, a z test is most commonly used for testing the statistical significance of the relevant parameter estimates or of the differences between parameter estimates, where a z value is computed based on the asymptotic…

Educational stakeholders are keen to know the magnitude and importance of different interventions. However, the way evidence is communicated to support understanding of the effectiveness of an intervention is controversial. Typically studies in education have used the standardised mean difference as a measure of the impact of interventions. This…

The purpose of this study was to investigate the relations among perceived instructional support (provision of relevance and involvement), subjective task value beliefs (utility, attainment, and intrinsic value), and engagement (behavioral and emotional) over the course of a semester for graduate students enrolled in an introductory research…

The authors examined 2 approaches for determining the required sample size of Welch's test for detecting equality of means when the greatest difference between any 2 group means is given. It is shown that the actual power obtained with the sample size of the suggested approach is consistently at least as great as the nominal power. However, the…